To circumvent some inherent problems in the conventional ECG, this research reinvestigates an ‘unassisted’ approach which enables ECG measurement without the placement of leads on the body. Employed in this research is a widely accepted assumption that the electrical activity of the heart may be represented, largely, by a 3-D time-varying current dipole (3D-CD). From the PhysioBank database, mECG and fECG data were obtained, and Singular Value Decomposition (SVD) was performed to estimate the time-varying Vector ECG dipole. To determine the sensing matrix responsible for transforming the activity of the 3D-CD into the potential distribution on the surface of the medium, the ECG vector dipole signals are used to excite a 3D-CD in water medium of a specific shape-containing-ellipsoid model(s) in COMSOL tool. The sensing matrix thereby estimated is then utilized to reconstruct the 3D-CD signals from the signals measured by the probes on the surface of the medium. Fairly low NRMSEs (Normalized Root-Mean-Squared Errors) are attained. The approach is also successfully extended to the case of two ellipsoids, one inside the other, representing a pregnant female subject. Low NRMSEs (Normalized Root-Mean-Squared Errors) are again observed.